-- chapter 10 -- pros: managing economies of scale in the...
TRANSCRIPT
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Managing Economies of Scale in the Managing Economies of Scale in the Supply Chain: Cycle InventorySupply Chain: Cycle Inventory
-- Chapter 10 --
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Why do we have inventory ?Why do we have inventory ?
Cons:
Significant cost– Space, capital, risk, …
So, the less, the better ?
Cons:
Significant cost– Space, capital, risk, …
So, the less, the better ?
Pros:To overcome the time and space lags between producers and consumersTo meet demand/supply uncertaintyTo achieve production /transportation economies/flexibilityTo take advantage of quantity purchase discountsTo improve service level (?)…
So, the more, the better ?
Pros:To overcome the time and space lags between producers and consumersTo meet demand/supply uncertaintyTo achieve production /transportation economies/flexibilityTo take advantage of quantity purchase discountsTo improve service level (?)…
So, the more, the better ?
Issues: - Overstocking vs. under-stocking- Supply chain responsiveness vs. efficiency
Issues: - Overstocking vs. under-stocking- Supply chain responsiveness vs. efficiency
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1. Understanding Inventory1. Understanding InventoryWhat types of inventory?– raw materials– WIP, parts, assembly components – finished goods …Where do we hold inventory?– Suppliers and manufacturers– warehouses and distribution centers– Retailers – Central location …When to have inventory?How much inventory should be held? …
Production Distribution
Transport
Customers
Transport Transport
Suppliers ResellersWhat to ship and
when?What to make
and when? What to
buy and when? 510 -
InventoryInventory DecisionsDecisionsInventory decision is affected by– Demand characteristics– Lead time– Number of products– Objective (service level, min costs, or the both?)– Cost structure– …
Goal:– Optimal matching supply and demand– 5 “R” principle
Decision criteria:– Traditional view: better tradeoff between customer service level and
inventory investment (cost)– Recent emphasis: increasing customer service AND reducing
inventory investment
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Cost structure of inventory: Cost structure of inventory:
Order costs
Fixed
Variable
InventoryCosts
Inventorycarrying
costs
Inventory investment
Insurance
Taxes
Obsolescence
Pilferage
Storagespace costs
Capitalcosts
Inventoryservicecosts
Inventoryrisk costs
Plant warehousesPublic warehouses
Rented warehousesCompany-owned
warehouses
Damage
Relocation costs
Maintenance& handling
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Is it possible to reduce cost Is it possible to reduce cost ANDAND improve service?improve service?
It can be achieved through– Effective inventory management
How to order?When to order?What to order?How much to order? …
– Supply chain management strategies
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2. The measure of inventory level2. The measure of inventory levelCycle Inventory– The average inventory that builds up in the SC when produced or
purchased lots are larger than those demanded by customerLot, or batch size: – quantity that a supply chain stage either produces or orders at a given
time– Q = lot or batch size of an order– D = demand per unit timeCycle inventory = Q/2 (depends directly on lot size)Average flow time = Avg inventory / Avg flow rateAverage flow time from cycle inventory = Q/(2D)
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Example:Example:
Q = 1000 unitsD = 100 units/day
Cycle inventory = Q/2 = 1000/2 = 500 = Avg inventory level from cycle inventoryAvg flow time = Q/2D = 1000/(2)(100) = 5 daysCycle inventory adds 5 days to the time a unit spends in the supply chainLower cycle inventory is better because:– Average flow time is lower– Working capital requirements are lower– Lower inventory holding costs
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Role of Cycle InventoryRole of Cycle Inventory
Cycle inventory is held primarily to take advantage of economies of scale in the supply chainSupply chain costs influenced by lot size:– Material cost = C– Fixed ordering cost = S– Holding cost = H = hC (h = cost of holding $1 in inventory for one year)
Primary role of cycle inventory is to allow different stages to purchase product in lot sizes that minimize the sum of material, ordering, and holding costsIdeally, cycle inventory decisions should consider costs across the entire supply chain, but in practice, each stage generally makes its own supply chain decisions – increases total cycle inventory and total costs in the supply chain
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How to decide lot size?How to decide lot size?
Lot sizing for a single product -- EOQAggregating multiple products in a single orderLot sizing with multiple products or customers– Lots are ordered and delivered independently for each
product– Lots are ordered and delivered jointly for all products– Lots are ordered and delivered jointly for a subset of
products
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TC = Order cost + Holding Cost + Purchasing Cost= (R/Q)S + (Q/2)hC + CR
Min TCQ
EOQ model:D -- Annual demand S -- Setup or Order CostC -- Cost per unith -- Holding cost per year as a
fraction of product costH -- Holding cost per unit per yearQ -- Lot Size, order quantityT -- Reorder intervaln – ordering frequencyS
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EOQ: Optimal lot size and reorder interval
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EOQ modelEOQ modelQuestions answered : How much to order?
When to order?
Optimal order quantity Optimal order quantity -- QQ
The most economic
order quantity (EOQ)
TCMinQ
Size of order
Annual cost(dollars)
Lowest total cost(EOQ)
Total cost
Inventorycarrying
cost
Ordering cost
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Example 10.1Example 10.1The Deskpro computer at Best Buy,
Demand, D = 12,000 computers per yearUnit cost, C = $500Holding cost, h = 0.2Fixed cost, S = $4,000/order
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Assumptions under the simple EOQ modelA continuous, constant, and known rate of demand.A constant and known replenishment cycle or lead time.A constant purchase price that is independent of the order quantity or time.A constant transportation cost that is independent of the order quantity or time.The satisfaction of all demand (no stockouts are permitted).Only one item in inventory, or at least no interaction among items.No limit on capital availability…
Removing some of the assumptions -- Variations of EOQ:- EOQ with backlog- EOQ with quantity discount- EOQ with continues replenishment- Stochastic inventory models- …
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Question:Can we further reduce the TC by reducing Q ?Question:Question:Can we further reduce the TC by reducing Q ?Can we further reduce the TC by reducing Q ?
If lot size reduce to Q = 200 units,Annual inventory cost = (D/Q)S + (Q/2)hC = $250,000– which is higher than TC=$97980 when Q*=980 units
(Example 10.2Example 10.2) To make it economically feasible to reduce lot size, the fixed cost associated with each lot would have to be reducedIf desired lot size Q = 200 units,The desired ordering cost, S = hCQ*2/2d = $166.70-- The store manager would have to reduce the ordering cost per lot from $4000
to $166.70 for a lot size of 200 to be optimal.
Observation: Q (< Q*)
⇒ Fixed cost ⇒ TC
Size of order
Annual cost(dollars)
Lowe s t total cos t(EOQ)
Total cost
Inventorycarrying
cost
Ordering cost
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Key Points from lot sizing by EOQKey Points from lot sizing by EOQ
In deciding the optimal lot size, the trade off is between order (setup) cost and holding cost.
If demand increases by a factor of k, it is optimal to increase batch size by a factor of (k1/2) and produce (order) a factor of (k1/2) as often. Flow time attributed to cycle inventory should decrease by a factor of (K1/2).
If lot size is to be reduced, one has to reduce fixed order cost. To reduce lot size by a factor of (k), order cost has to be reduced by a factor of (k2).
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3. Strategies to improve SC performance while lowering cycle inventory
1) Aggregation (across products, supply points, delivery points …)
2) Lot sizing with aggregation strategies3) Quantity discounts4) Short term discounting: trade promotions
Successful cases– Wal-Mart: 3 day replenishment cycle – 7-11 Japan: Multiple daily replenishment
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Aggregating Multiple ProductsAggregating Multiple Productsin a Single Orderin a Single Order
Transportation is a significant contributor to the fixed cost per orderCan possibly combine shipments of different products from the same supplier– same overall fixed cost– shared over more than one product– effective fixed cost is reduced for each product– lot size for each product can be reduced
Can also have a single delivery coming from multiple suppliers or a single truck delivering to multiple retailersAggregating across products, retailers, or suppliers in a single order allows for a reduction in lot size for individual products because fixed ordering and transportation costs are now spread across multiple products, retailers, or suppliers
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Example: Aggregating Multiple Products Example: Aggregating Multiple Products in a Single Orderin a Single Order
Suppose there are 4 computer products in the previous example: Deskpro, Litepro, Medpro, and Heavpro. Assume demand for each is 1000 units per month
If each product is ordered separately:– Q* = 980 units for each product– Total cycle inventory = 4(Q/2) = (4)(980)/2 = 1960 units
Aggregate orders of all four products:– Combined Q* = 1960 units– For each product: Q* = 1960/4 = 490– Cycle inventory for each product is reduced to 490/2 = 245– Total cycle inventory = 1960/2 = 980 units– Average flow time, inventory holding costs will be reduced
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Lot Sizing with Aggregation StrategyLot Sizing with Aggregation StrategyWhy?
– In practice, the fixed ordering cost is dependent at least in part on the variety associated with an order of multiple models
A portion of the cost is related to transportation (independent of variety)A portion of the cost is related to loading and receiving (not independent of variety)
– Aggregating across products, retailers, or suppliers in a single order allows for a reduction in lot size for individual products because fixed ordering and transportation costs are now spread across multiple products, retailers, or suppliers.
– Service ?
How? -- Three scenarios:– Lots are ordered and delivered independently for each product– Lots are ordered and delivered jointly for all three models– Lots are ordered and delivered jointly for a selected subset of models
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Example 10.3 Example 10.3 –– Best BuyBest Buy
The Deskpro computer at Best Buy, three models,– Demand per year: DL = 12,000; DM = 1,200; DH = 120
– Product specific order cost: sL = sM = sH = $1,000
– Unit cost: CL = CM = CH = $500– Common transportation cost: S = $4,000
– Holding cost: h = 0.2
Delivery options:No Aggregation: Each product ordered separatelyComplete Aggregation: All products delivered on each truckTailored Aggregation: Selected subsets of products on each truck
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Option 1Option 1: No Aggregation : No Aggregation -- Order each Order each product independentlyproduct independently
Example 10.3 Litepro Medpro Heavypro
Demand per year
12,000
1,200
120
Fixed cost / order
$5,000
$5,000
$5,000
Optimal order size (Q*)
1,095
346
110
Cycle inventory (Q*/2)
548
173
55
Order frequency (n*)
11.0 / year
3.5 / year
1.1 / year
Annual cost (TC*)
$109,544
$34,642
$10,954
Total cost = $155,140
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Option 2:Option 2: Complete Aggregation: Order all Complete Aggregation: Order all products jointlyproducts jointly
Annual order cost = 9.75×$7,000 = $68,250
Annual total cost = $136,528
The combined fixed order cost: S*= S + SL + SM + SH
TC = {Annual Order Cost}+{Annual Holding Cost} =
The optimal ordering frequency, n* =
Example 10.4
Litepro Medpro Heavypro
Demand per year
12,000 1,200 120
Order frequency n*
9.75/year 9.75/year 9.75/year
Optimal order size Q*
1,230 123 12.3
Cycle inventory(Q*
/2)
615 61.5 6.15
Annual holding cost
$61,512 $6,151 $615
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Option 3:Option 3: Tailored Aggregation: Tailored Aggregation: Ordering Selected SubsetsOrdering Selected Subsets
Discussion:
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Step 1: Identify most frequently ordered product
Step 2: Identify frequency of other products as a multiple
Step 3: Recalculate ordering frequency of most frequently ordered product
Step 4: Identify ordering frequency of all products
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Tailored Aggregation: Order selected Tailored Aggregation: Order selected subsetssubsets
Example 10.5 Litepro Medpro Heavypro
Demand per year
12,000 1,200 120
Order frequency n*
10.8/year 5.4/year 2.16/year
Optimal order size Q*
1,111 222 56
Cycle inventory
555.5 111 28
Annual holding cost
$55,556 $11,111 $2,778
Annual order cost = $61,560Total annual cost = $131,004
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Product specific order cost = $1000 Total cost Cycle Inv.
Product specific order cost = $3000
No Aggregation $155,140 776 $183,564
Complete Aggregation $136,528 682.65 $186,097
Tailored Aggregation $131,004 694.5 $165,233
Aggregation reducesthe total cost AND cycle inventory ! A
Impact of product specific order cost
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Lessons From AggregationLessons From Aggregation
Aggregation allows firm to lower lot size without increasing costA key to reduce lot size without increasing costs is to reduce the fixed cost associated with each lot, which can be achieved by reducing the fixed cost itself or by aggregating across multipleproducts, customers or suppliers.
Complete aggregation is effective if product specific fixed cost is a small fraction of joint fixed costTailored aggregation is effective if product specific fixed cost is large fraction of joint fixed costTailored aggregation can also be used when a single truck makes deliveries to multiple customers, some large and some small.
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Strategy 3Strategy 3: Quantity Discounts: Quantity Discounts
Commonly used in B2B transactions
Types of Quantity Discount– Lot size based (based on the quantity ordered in a single lot)
All unitsMarginal unit
– Volume based (based on the total quantity purchased over a given period)
Questions:– How should buyer react?– How to determine appropriate discounting schemes? – What is the impact of quantity discounts on the supply Chain?– How to use the QD strategy to improve SC performance?
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Example 10.6Example 10.6 [Review yourself !!!]Drugs Online (DO) – an online retailer of prescription
drugs and health supplements
D = 120,000/yr. S = $100/lot, h = 0.2
The manager wants to know how many bottles to order in each lot?
$2.92Over 10,000$2.965001-10,000$3.000-5,000Unit PriceOrder quantity
By using the EOQ model with quantity discount,
QQ* * = 10,001 units= 10,001 units (with the unit price = $2.96)
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The Method for AllThe Method for All--Unit Quantity Unit Quantity DiscountsDiscounts
Evaluate EOQ for price in range qi to qi+11. If qi ≤ EOQ < qi+1 ,
evaluate cost of ordering EOQ 2. If EOQ < qi,
evaluate cost of ordering qi
3. If EOQ ≥ qi+1 , evaluate cost of ordering qi+1
Evaluate minimum cost over all price ranges
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Impacts of Quantity Discounts Impacts of Quantity Discounts ……(recalling the beer game …)Quantity discounts encourage large order quantities and lead a significant buildup of cycle inventory Retailers are encouraged to increase the size of their ordersAverage inventory (cycle inventory) in the supply chain is increasedAverage flow time is increased
So, why quantity discount?Quantity discount can be valuable in a SC to improve chain coordinationand reduce the total chain cost
But How ?But How ?
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Coordination for Commodity ProductsCoordination for Commodity ProductsCommodity product – the market sets the price and the firms objective is to lower costsDO makes its lot sizing decisions (of vitamins) based on its own costs
Supplier --Manufacturer
Retailer -- DO Customers
Retail side:D = 120,000 bottles/yrSR = $100/order, hR = 0.2, CR =$3/bottleRetailer’s optimal lot size: Q* = 6,324Retailer cost = $3,795
Supplier sideSS = $250, hS = 0.2, CS = $2Supplier cost = (120,000/6324)x250+(6324/2)x2x0.2 = $6,009
Supply chain cost = 3795 + 6009 = $9,804
p & D
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If DoIf Do’’s Order Size = 9165s Order Size = 9165units
Observation:– If DO order 9165, the total chain saves $638 and the supplier saves
$902, but retailer pays $624 more !Question:– How to convince DO to take the order size of 9165?
Supplier --Manufacturer
Retailer -- DO Customers
Retailer cost(= $3,795 + $264)= $4,059
Supplier Cost (= $6,009 - $902)= $5,107
Supply chain cost = $9165 (= $9,804 - $638)
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The SC Solution:- The supplier offer lot size-based quantity discounts incentive
< 9165, $3> 9165, $2.9978
– The resulted optimal order size at DO: Q* = 9165, by using EOQ model with quantity discount
– The manufacturer returns $264 (=$4059-3795) to DO as material cost reduction to make it optimal for DO to order 9165 bottles
– Passing some fixed cost to retailer (enough that he raises order size from 6324 to 9165)
After all– Retailer cost = $4,059 – 264 = $3795 (no change); – Supplier cost = $5,106 + 264 = 5370 (save $639); – Supply chain cost = $9,165 (save $639).
Use Quantity Discount Strategy to achieve the Chain Coordination and the Chain Cost Reduction
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Key point:Key point:
For commodity products for which price is set by the market, manufacturers can use lot size-based quantity discounts to achieve coordination in the supply chain and decrease supply chain cost. Lot size-based discounts, however, increase cycle inventory in the supply chain.
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Quantity Discounts When Firm has Market Quantity Discounts When Firm has Market PowerPower
A new vitamin – Vitaherb, no competitorsThe sale price at DO will influence demandThe demand curve is given by 360,000 - 60,000p
Production cost at the manufacturer Cs = $2/bottleManufacturer needs to decide the price to charge Do, pR,, and DO needs to decide the price to charge customers, p.
Manufacturer DO Customerp=?pR=?Cs=$2 (D=360-60p)
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ProfM=pR(360-60p)-(360-60p)CS=pR(360-60p)-(360-60p)x$2
(**)=pR[360-60(3+0.5pR)]-720+120(3+0.5pR)=-30pR
2+240pR-360d(ProfM)/d(pR)=-60pR+240=0pR*=$4, ProfM=120,000,
Manufacturer DO Customerp=?pR=?Cs=$2
IF the two stages make the pricing decision independently
ProfR = p(360-60p)-(360-60p)pR
d(ProfR)/d(p)=360-120p+60pR=0P*=(360+60pR)/120=3+0.5pR (**)
Total Chain Profit = $180,000, Demand = 60,000
P* = 3+0.5pR = 3+0.5x4=$5, ProfR=$60,000,
IF the two stages coordinate the pricing decisions
• p=pR=$4, then ProfR=$60,000, ProfM=180,000, and • Total Chain Profit = $240,000 (increased by $60,000), Demand=120,000
(D=360-60p)
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Question:Question:How can the manufacturer achieve the coordinated How can the manufacturer achieve the coordinated solution and maximize supply chain profit?solution and maximize supply chain profit?
Design a volume discount scheme (see the text page 161 for detail, if interested.) that achieves the coordinated solution.– < 120,000, $4
> 120,000, $3.5– Following this discount scheme, the DO’s optimal order Q*=120,000 and p*=$4
Design a two-part tariff that achieves the coordinated solution.– Ask DO (1) a up-front cost of $180,000, and (2) pR=$2
Key PointWhen products for which the firm has market power, two-part tariffs or volume-based quantity discounts can be used to achieve coordination in supply chain and maximize supply chain profit
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Lessons From Discounting SchemesLessons From Discounting Schemes
Lot size based discounts increase lot size and cycle inventory in the supply chainLot size based discounts are justified to achieve coordination for commodity productsVolume based discounts with some fixed cost passed on to retailer are more effective in generalWhen products for which the firm has market power, the approaches of volume-based quantity discounts or two-part tariffs can be used to achieve coordination in supply chain and maximizesupply chain profit
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Strategy 4Strategy 4: Short Term Discounting: Short Term DiscountingGoal – to influence retailers to act in a way that helps the manufacturer achieve its objective– Induce retailers to use price discounts– Shift inventory from the manufacturer to the retailer and the
customer– Defend a brand against competition
Questions– What is the impact of a trade promotion on the behavior of the
retailer and the performance of the supply chain?– How should a retailer react to a trade promotion a manufacturer
offers?
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Impact of a trade promotionImpact of a trade promotion
A manufacturer lowers the price of a product
Manufacturer RetailerDO
End Customer
• no in purchase• forward buy • inventory • future cost
Supply Chain
• purchase • sales
• cycle inventory • flow time • demand variability
• Profit
• sales • inventory
Size of forward buy?How should the retail react?
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Forward buy of the retailerForward buy of the retailer
Q*: Normal order quantityC: Normal unit costd: Short term discountR: Annual demandh: Cost of holding $1 per yearQd: Short term order quantity
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Short Term Discounts: Forward buyingShort Term Discounts: Forward buying
Example 10.8Normal order size, Q* = 6,324 bottles Normal cost, C = $3 per bottleDiscount per tube, d = $0.15Annual demand, R = 120,000Holding cost, h = 0.2
Before promotion: Cycle inventory = Q*/2 = 6324/2 = 3162 bottlesAverage flow time = Q*/2R = 6234 /(2x120000) =
0.3162 mths (≅9 days)Promotion: Qd = 38236
Forward buy = Qd – Q* = 38263-6324 = 31912 bottles
After promotion: Cycle inventory = Qd/2 = 38236/2 = 19118 bottles (≅6 times)
(Opt. Buy for Retailer) Average flow time = Qd/2R = 1.9118 mths(≅5 times)
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Key point:
Trade promotions lead to a significant increase in lot size and cycle inventory because of forward buying by the retailer. This generally results in reduced supply chain profits unless the trade promotion reduces demand fluctuation
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Promotion pass through to consumersPromotion pass through to consumersIt may be optimal to the retailer to pass through some (not entire) of the discount to the end customer
Demand at retailer DO: 300,000 - 60,000pNormal supplier price, PR = $3.00
Max ProfR = p(300,000-60,000p)-(300,000-60,000p)PR
300,000 – 120,000p + 60,000PR = 0p = (300,000 + 60,000PR) / 120,000
Optimal retail price: p = $4.00Customer demand: RR = 300,000 – 60,000p
= 60,000
Promotion discount = $0.15, thus PR = $2.85Optimal retail price: p = $3.925 Customer demand: D = 64,500
Retailer passes through half the promotion discount and demand increases by 7.5%
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Key point:Key point:
Faced with a short-term discount, it is optimal for retailers to pass through only a fraction of the discount to the customer, keeping the rest for themselves. Simultaneously, it is optimal for the retailer to increase the purchase lot size and forward buy for future period. This lead to an increase of cycle inventory in the supply chain as the result of a trade promotion without a significant increase in customer demand.
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Summary of Learning ObjectivesSummary of Learning Objectives
How are the appropriate costs balanced to choose the optimal amount of cycle inventory in the supply chain?What are the effects of quantity discounts on lot size and cycle inventory?What are appropriate discounting schemes for the supply chain, taking into account cycle inventory?What are the effects of trade promotions on lot size and cycle inventory?What are managerial levers that can reduce lot size and cycle inventory without increasing costs?